In a ` A B C ,D` and `E` are points on sides `A Ba n dA C` respectively such that `B D=C Edot` If `/_B=/_C ,` show that `D E B Cdot`

In a A B C ,D and E are points on sides A B a n d A C respectively such that B D=C E . If /_B=/_C , show that DE || BC .

In A B C ,\ D and E are points on sides A B and A C respectively such that A DxxE C=A ExxD B . Prove that D E B C .

In a A B C , D and E are points on the sides A B and A C respectively such that D E || B C If A D=6\ c m , D B=9\ c m and A E=8\ c m , find A C .

In a A B C , D and E are points on the sides A B and A C respectively such that D E// B C If A D=4 , A E=8 , D B=x-4 , and E C=3x-19 , find x .

In Figure, A B C is a triangle in which A B=A Cdot Point D and E are points on the sides AB and AC respectively such that A D=A Edot Show that the points B , C , E and D are concyclic.

In a A B C ,\ \ D\ a n d\ E are points on the sides A B and A C respectively. For each of the following cases show that D E// B C : A B=12\ c m ,\ \ A D=8\ c m ,\ \ A E=12\ c m\ a n d\ A C=18\ c m .

In a A B C , D and E are points on the sides A B and A C respectively such that D E// B C If A D=2\ c m , A B=6\ c m and A C=9\ c m , find A E . .

In a A B C , D a n d E are points on the sides A B and A C respectively. For each of the following cases show that D E B C : A B=12 c m , A D=8 c m , A E=12 c m a n d A C=18 c m . (ii) A B=5. 6 c m , A D=1. 4 c m , A C=7. 2 c m a n d A E=1. 8 cm

In Figure, D , E are points on sides A B and A C respectively of A B C , such that a r( B C E)=a r( B C D)dot Show that DE ll BC .

D and E are points on sides AB and AC respectively of DeltaA B C such that a r\ (D B C)\ =\ a r\ (E B C) . Prove that D E\ ||\ B C .